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JEE Main 20206 SeptemberMorning Shift
Exam
JEE Main
Year
2020
Date
6 September
Shift
Morning Shift
Subject
Mathematics
Chapter
Application of Derivatives

JEE Main 2020 · 6 September · Morning Shift · Mathematics · Application of Derivatives

Let AD and BC be two vertical poles at AandB respectively on a...

Let ADAD and BCBC be two vertical poles at AandBA\text{and}B respectively on a horizontal ground. If AD=8mAD = 8m, BC=11mBC = 11m, AB=10m;AB = 10m; then the distance (in meters) of a point MM lying in between ABAB from the point AA such that MD2+MC2{MD}^{2} + {MC}^{2} is minimums, is__Let AD and BC be two vertical poles at AandB respectively on a horizontal ground. If AD = 8m , BC = 11m , AB = 10m;

Correct answer

5

Step-by-step solution

Let AD and BC be two vertical poles at AandB respectively on a horizontal ground. If AD = 8m , BC = 11m , AB = 10m;

Let AM=xandS=MD2+MC2AM = x\text{and}S = {MD}^{2} + {MC}^{2}

So, MD2+MC2=64+x2+121+(10−x)2{MD}^{2} + {MC}^{2} = 64 + {x}^{2} + 121 + ( 10 - x{)}^{2}

⇒S=285−20x+2x2⇒ S = 285 - 20x + 2{x}^{2}

dSdx=−20+4x⇒dSdx=0⇒x=5\dfrac{dS}{dx} = - 20 + 4x ⇒ \dfrac{dS}{dx} = 0 ⇒ x = 5

d2Sdx2=4=+ve\dfrac{{d}^{2}S}{{dx}^{2}} = 4 = + ve

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